You are planning your retirement in 10 years. You currently have $150,000 in a bond account and...

Question:

You are planning your retirement in 10 years. You currently have {eq}\$150,000 {/eq} in a bond account and {eq}\$450,000 {/eq} in a stock account. You plan to add {eq}\$9,000 {/eq} per year at the end of each of the next 10 years to your bond account. The stock account will earn an 11.5 percent return and the bond account will earn a 7.5 percent return. When you retire, you plan to withdraw an equal amount for each of the next 25 years m the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 6.75 percent. How much can you withdraw each year?

Annuity:

People are recommended to include an annuity in their retirement portfolio as an annuity can produce a series of payments during a specific period. In practice, annuity payments can be grown at a constant rate to beat the inflation.

Answer and Explanation: 1

Summary:

Bond account:

  • Available fund = $150,000
  • Annual deposit = $9,000
  • Number of deposits = 10
  • Annual interest rate (I1) = 7.5%

Stock account:

  • Available fund = $450,000
  • Annual interest rate (I2) = 11.5%


Determine the value of the stock account after 10 years:

{eq}Value_{stock} = \displaystyle Availabe\:fund_{stock}\times (1 + I2)^N {/eq}

{eq}Value_{stock} = \displaystyle \$450,000\times (1 + 11.5\%)^{10} {/eq}

{eq}Value_{stock} = $1,336,476.07 {/eq}

Determine the value of the bond account after 10 years:

{eq}Value_{bond} = \displaystyle Available\:fund_{bond}\times (1 + I1)^N + \displaystyle Deposit\times \frac{(1 + I1)^N - 1}{I1} {/eq}

{eq}Value_{bond} = \displaystyle \$150,000\times (1 + 7.5\%)^{10} + \displaystyle \$9,000\times \frac{(1 + 7.5\%)^{10} - 1}{7.5\%} {/eq}

{eq}Value_{bond} = $309,154.73 + $127,323.79 {/eq}

{eq}Value_{bond} = $436,478.52 {/eq}

Determine the total amount of money available after 10 years:

{eq}Total\:fund = Value_{stock} + Value_{bond} {/eq}

{eq}Total\:fund = $1,336,476.07 + $436,478.52 {/eq}

{eq}Total\:fund = $1,772,954.59 {/eq}

Determine the annual withdrawal within 25 years:

{eq}Withdrawal = \displaystyle \frac{Total\:fund}{\displaystyle\frac{1-(1 + I)^{-N}}{I}} {/eq}

{eq}Withdrawal = \displaystyle \frac{\$1,772,954.59}{\displaystyle\frac{1-(1 + 6.75\%)^{-25}}{6.75\%}} {/eq}

{eq}Withdrawal = \$148,727.69 {/eq}

The investor can withdraw an equal amount of $148,727.69 per year within 25 years after the retirement.


Learn more about this topic:

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What is Annuity? - Definition & Formula

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Chapter 2 / Lesson 7
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Learn about annuities. Understand what an annuity is, examine the annuity formula and learn how to calculate its future value, and see examples of annuities.


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